Properties

Label 930.2.be.b.37.15
Level $930$
Weight $2$
Character 930.37
Analytic conductor $7.426$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(37,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.be (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.15
Character \(\chi\) \(=\) 930.37
Dual form 930.2.be.b.553.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23583 - 0.0323803i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.933337 - 3.48326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23583 - 0.0323803i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.933337 - 3.48326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.60387 + 1.55808i) q^{10} +(0.937738 + 0.541403i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(0.708853 - 0.189937i) q^{13} +(3.12301 - 1.80307i) q^{14} +(-0.547399 + 2.16803i) q^{15} -1.00000 q^{16} +(1.82022 + 0.487725i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(2.84515 - 1.64265i) q^{19} +(0.0323803 + 2.23583i) q^{20} +(3.12301 + 1.80307i) q^{21} +(0.280251 + 1.04591i) q^{22} +(4.61672 + 4.61672i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.99790 - 0.144794i) q^{25} +(0.635540 + 0.366929i) q^{26} +(0.707107 - 0.707107i) q^{27} +(3.48326 + 0.933337i) q^{28} -4.96922 q^{29} +(-1.92010 + 1.14596i) q^{30} +(4.58282 - 3.16192i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.765660 + 0.765660i) q^{33} +(0.942213 + 1.63196i) q^{34} +(1.97400 - 7.81822i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.58688 - 2.03290i) q^{37} +(3.17335 + 0.850297i) q^{38} +0.733859i q^{39} +(-1.55808 + 1.60387i) q^{40} +(-1.80041 + 3.11840i) q^{41} +(0.933337 + 3.48326i) q^{42} +(-1.95268 + 7.28750i) q^{43} +(-0.541403 + 0.937738i) q^{44} +(-1.95248 - 1.08987i) q^{45} +6.52903i q^{46} +(-1.04488 - 1.04488i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-5.19982 - 3.00212i) q^{49} +(3.63644 + 3.43167i) q^{50} +(-0.942213 + 1.63196i) q^{51} +(0.189937 + 0.708853i) q^{52} +(1.37392 - 0.368140i) q^{53} +1.00000 q^{54} +(2.11416 + 1.18012i) q^{55} +(1.80307 + 3.12301i) q^{56} +(0.850297 + 3.17335i) q^{57} +(-3.51377 - 3.51377i) q^{58} +(5.72773 - 3.30690i) q^{59} +(-2.16803 - 0.547399i) q^{60} -5.17239i q^{61} +(5.47636 + 1.00473i) q^{62} +(-2.54992 + 2.54992i) q^{63} -1.00000i q^{64} +(1.57873 - 0.447620i) q^{65} -1.08281 q^{66} +(1.63393 - 0.437811i) q^{67} +(-0.487725 + 1.82022i) q^{68} +(-5.65431 + 3.26452i) q^{69} +(6.92414 - 4.13249i) q^{70} +(-6.67279 + 11.5576i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-14.4276 + 3.86587i) q^{73} +(-3.92726 - 6.80221i) q^{74} +(-1.15369 + 4.86508i) q^{75} +(1.64265 + 2.84515i) q^{76} +(2.76108 - 2.76108i) q^{77} +(-0.518917 + 0.518917i) q^{78} +(4.54232 + 7.86753i) q^{79} +(-2.23583 + 0.0323803i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-3.47813 + 0.931962i) q^{82} +(-5.99147 + 1.60541i) q^{83} +(-1.80307 + 3.12301i) q^{84} +(4.08549 + 1.03153i) q^{85} +(-6.53380 + 3.77229i) q^{86} +(1.28613 - 4.79990i) q^{87} +(-1.04591 + 0.280251i) q^{88} -0.807115 q^{89} +(-0.609953 - 2.15127i) q^{90} -2.64640i q^{91} +(-4.61672 + 4.61672i) q^{92} +(1.86806 + 5.24503i) q^{93} -1.47769i q^{94} +(6.30809 - 3.76481i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.50771 - 5.50771i) q^{97} +(-1.55401 - 5.79964i) q^{98} +(-0.541403 - 0.937738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 1.00000i 0.500000i
\(5\) 2.23583 0.0323803i 0.999895 0.0144809i
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 0.933337 3.48326i 0.352768 1.31655i −0.530501 0.847684i \(-0.677996\pi\)
0.883270 0.468865i \(-0.155337\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 1.60387 + 1.55808i 0.507188 + 0.492707i
\(11\) 0.937738 + 0.541403i 0.282739 + 0.163239i 0.634663 0.772789i \(-0.281139\pi\)
−0.351924 + 0.936029i \(0.614472\pi\)
\(12\) −0.965926 0.258819i −0.278839 0.0747146i
\(13\) 0.708853 0.189937i 0.196600 0.0526789i −0.159175 0.987250i \(-0.550883\pi\)
0.355776 + 0.934571i \(0.384217\pi\)
\(14\) 3.12301 1.80307i 0.834659 0.481890i
\(15\) −0.547399 + 2.16803i −0.141338 + 0.559783i
\(16\) −1.00000 −0.250000
\(17\) 1.82022 + 0.487725i 0.441467 + 0.118291i 0.472704 0.881221i \(-0.343278\pi\)
−0.0312370 + 0.999512i \(0.509945\pi\)
\(18\) −0.258819 0.965926i −0.0610042 0.227671i
\(19\) 2.84515 1.64265i 0.652722 0.376849i −0.136776 0.990602i \(-0.543674\pi\)
0.789498 + 0.613753i \(0.210341\pi\)
\(20\) 0.0323803 + 2.23583i 0.00724045 + 0.499948i
\(21\) 3.12301 + 1.80307i 0.681496 + 0.393462i
\(22\) 0.280251 + 1.04591i 0.0597497 + 0.222989i
\(23\) 4.61672 + 4.61672i 0.962653 + 0.962653i 0.999327 0.0366741i \(-0.0116763\pi\)
−0.0366741 + 0.999327i \(0.511676\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 4.99790 0.144794i 0.999581 0.0289588i
\(26\) 0.635540 + 0.366929i 0.124640 + 0.0719608i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 3.48326 + 0.933337i 0.658275 + 0.176384i
\(29\) −4.96922 −0.922761 −0.461380 0.887202i \(-0.652646\pi\)
−0.461380 + 0.887202i \(0.652646\pi\)
\(30\) −1.92010 + 1.14596i −0.350560 + 0.209223i
\(31\) 4.58282 3.16192i 0.823099 0.567898i
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −0.765660 + 0.765660i −0.133284 + 0.133284i
\(34\) 0.942213 + 1.63196i 0.161588 + 0.279879i
\(35\) 1.97400 7.81822i 0.333666 1.32152i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −7.58688 2.03290i −1.24727 0.334206i −0.425992 0.904727i \(-0.640075\pi\)
−0.821283 + 0.570521i \(0.806741\pi\)
\(38\) 3.17335 + 0.850297i 0.514786 + 0.137936i
\(39\) 0.733859i 0.117511i
\(40\) −1.55808 + 1.60387i −0.246354 + 0.253594i
\(41\) −1.80041 + 3.11840i −0.281177 + 0.487013i −0.971675 0.236321i \(-0.924058\pi\)
0.690498 + 0.723334i \(0.257391\pi\)
\(42\) 0.933337 + 3.48326i 0.144017 + 0.537479i
\(43\) −1.95268 + 7.28750i −0.297781 + 1.11133i 0.641202 + 0.767372i \(0.278436\pi\)
−0.938984 + 0.343962i \(0.888231\pi\)
\(44\) −0.541403 + 0.937738i −0.0816196 + 0.141369i
\(45\) −1.95248 1.08987i −0.291058 0.162469i
\(46\) 6.52903i 0.962653i
\(47\) −1.04488 1.04488i −0.152412 0.152412i 0.626782 0.779194i \(-0.284372\pi\)
−0.779194 + 0.626782i \(0.784372\pi\)
\(48\) 0.258819 0.965926i 0.0373573 0.139419i
\(49\) −5.19982 3.00212i −0.742831 0.428874i
\(50\) 3.63644 + 3.43167i 0.514270 + 0.485311i
\(51\) −0.942213 + 1.63196i −0.131936 + 0.228520i
\(52\) 0.189937 + 0.708853i 0.0263395 + 0.0983002i
\(53\) 1.37392 0.368140i 0.188722 0.0505679i −0.163220 0.986590i \(-0.552188\pi\)
0.351942 + 0.936022i \(0.385521\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.11416 + 1.18012i 0.285073 + 0.159128i
\(56\) 1.80307 + 3.12301i 0.240945 + 0.417329i
\(57\) 0.850297 + 3.17335i 0.112625 + 0.420321i
\(58\) −3.51377 3.51377i −0.461380 0.461380i
\(59\) 5.72773 3.30690i 0.745686 0.430522i −0.0784468 0.996918i \(-0.524996\pi\)
0.824133 + 0.566396i \(0.191663\pi\)
\(60\) −2.16803 0.547399i −0.279891 0.0706690i
\(61\) 5.17239i 0.662256i −0.943586 0.331128i \(-0.892571\pi\)
0.943586 0.331128i \(-0.107429\pi\)
\(62\) 5.47636 + 1.00473i 0.695498 + 0.127601i
\(63\) −2.54992 + 2.54992i −0.321260 + 0.321260i
\(64\) 1.00000i 0.125000i
\(65\) 1.57873 0.447620i 0.195817 0.0555204i
\(66\) −1.08281 −0.133284
\(67\) 1.63393 0.437811i 0.199617 0.0534872i −0.157625 0.987499i \(-0.550384\pi\)
0.357242 + 0.934012i \(0.383717\pi\)
\(68\) −0.487725 + 1.82022i −0.0591454 + 0.220733i
\(69\) −5.65431 + 3.26452i −0.680699 + 0.393002i
\(70\) 6.92414 4.13249i 0.827593 0.493927i
\(71\) −6.67279 + 11.5576i −0.791914 + 1.37164i 0.132866 + 0.991134i \(0.457582\pi\)
−0.924780 + 0.380502i \(0.875751\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) −14.4276 + 3.86587i −1.68862 + 0.452466i −0.970034 0.242968i \(-0.921879\pi\)
−0.718591 + 0.695433i \(0.755212\pi\)
\(74\) −3.92726 6.80221i −0.456534 0.790741i
\(75\) −1.15369 + 4.86508i −0.133217 + 0.561771i
\(76\) 1.64265 + 2.84515i 0.188425 + 0.326361i
\(77\) 2.76108 2.76108i 0.314654 0.314654i
\(78\) −0.518917 + 0.518917i −0.0587557 + 0.0587557i
\(79\) 4.54232 + 7.86753i 0.511051 + 0.885166i 0.999918 + 0.0128080i \(0.00407702\pi\)
−0.488867 + 0.872358i \(0.662590\pi\)
\(80\) −2.23583 + 0.0323803i −0.249974 + 0.00362023i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −3.47813 + 0.931962i −0.384095 + 0.102918i
\(83\) −5.99147 + 1.60541i −0.657649 + 0.176217i −0.572185 0.820125i \(-0.693904\pi\)
−0.0854644 + 0.996341i \(0.527237\pi\)
\(84\) −1.80307 + 3.12301i −0.196731 + 0.340748i
\(85\) 4.08549 + 1.03153i 0.443134 + 0.111885i
\(86\) −6.53380 + 3.77229i −0.704557 + 0.406776i
\(87\) 1.28613 4.79990i 0.137887 0.514603i
\(88\) −1.04591 + 0.280251i −0.111494 + 0.0298749i
\(89\) −0.807115 −0.0855541 −0.0427770 0.999085i \(-0.513621\pi\)
−0.0427770 + 0.999085i \(0.513621\pi\)
\(90\) −0.609953 2.15127i −0.0642947 0.226764i
\(91\) 2.64640i 0.277418i
\(92\) −4.61672 + 4.61672i −0.481327 + 0.481327i
\(93\) 1.86806 + 5.24503i 0.193709 + 0.543884i
\(94\) 1.47769i 0.152412i
\(95\) 6.30809 3.76481i 0.647197 0.386262i
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) −5.50771 5.50771i −0.559224 0.559224i 0.369863 0.929086i \(-0.379405\pi\)
−0.929086 + 0.369863i \(0.879405\pi\)
\(98\) −1.55401 5.79964i −0.156979 0.585852i
\(99\) −0.541403 0.937738i −0.0544131 0.0942462i
\(100\) 0.144794 + 4.99790i 0.0144794 + 0.499790i
\(101\) 2.86245 0.284825 0.142412 0.989807i \(-0.454514\pi\)
0.142412 + 0.989807i \(0.454514\pi\)
\(102\) −1.82022 + 0.487725i −0.180228 + 0.0482920i
\(103\) −2.21078 8.25075i −0.217835 0.812971i −0.985149 0.171700i \(-0.945074\pi\)
0.767314 0.641271i \(-0.221593\pi\)
\(104\) −0.366929 + 0.635540i −0.0359804 + 0.0623199i
\(105\) 7.04091 + 3.93024i 0.687122 + 0.383552i
\(106\) 1.23182 + 0.711191i 0.119645 + 0.0690770i
\(107\) 4.36689 16.2974i 0.422163 1.57553i −0.347879 0.937540i \(-0.613098\pi\)
0.770042 0.637994i \(-0.220235\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 11.1442i 1.06742i 0.845668 + 0.533709i \(0.179202\pi\)
−0.845668 + 0.533709i \(0.820798\pi\)
\(110\) 0.660461 + 2.32941i 0.0629725 + 0.222100i
\(111\) 3.92726 6.80221i 0.372759 0.645637i
\(112\) −0.933337 + 3.48326i −0.0881921 + 0.329137i
\(113\) −0.136270 0.508565i −0.0128192 0.0478418i 0.959220 0.282661i \(-0.0912170\pi\)
−0.972039 + 0.234819i \(0.924550\pi\)
\(114\) −1.64265 + 2.84515i −0.153848 + 0.266473i
\(115\) 10.4717 + 10.1727i 0.976492 + 0.948612i
\(116\) 4.96922i 0.461380i
\(117\) −0.708853 0.189937i −0.0655335 0.0175596i
\(118\) 6.38845 + 1.71178i 0.588104 + 0.157582i
\(119\) 3.39775 5.88507i 0.311471 0.539484i
\(120\) −1.14596 1.92010i −0.104611 0.175280i
\(121\) −4.91376 8.51089i −0.446706 0.773717i
\(122\) 3.65743 3.65743i 0.331128 0.331128i
\(123\) −2.54617 2.54617i −0.229580 0.229580i
\(124\) 3.16192 + 4.58282i 0.283949 + 0.411550i
\(125\) 11.1698 0.485568i 0.999056 0.0434306i
\(126\) −3.60614 −0.321260
\(127\) −10.2509 2.74673i −0.909625 0.243733i −0.226480 0.974016i \(-0.572722\pi\)
−0.683145 + 0.730283i \(0.739388\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −6.53380 3.77229i −0.575269 0.332132i
\(130\) 1.43284 + 0.799814i 0.125669 + 0.0701483i
\(131\) 7.12749 + 12.3452i 0.622732 + 1.07860i 0.988975 + 0.148084i \(0.0473104\pi\)
−0.366243 + 0.930519i \(0.619356\pi\)
\(132\) −0.765660 0.765660i −0.0666421 0.0666421i
\(133\) −3.06629 11.4435i −0.265881 0.992281i
\(134\) 1.46495 + 0.845786i 0.126552 + 0.0730648i
\(135\) 1.55808 1.60387i 0.134098 0.138039i
\(136\) −1.63196 + 0.942213i −0.139939 + 0.0807941i
\(137\) −2.38978 8.91876i −0.204172 0.761981i −0.989700 0.143155i \(-0.954275\pi\)
0.785528 0.618826i \(-0.212391\pi\)
\(138\) −6.30656 1.68984i −0.536850 0.143849i
\(139\) 5.27800 0.447674 0.223837 0.974627i \(-0.428142\pi\)
0.223837 + 0.974627i \(0.428142\pi\)
\(140\) 7.81822 + 1.97400i 0.660760 + 0.166833i
\(141\) 1.27972 0.738845i 0.107772 0.0622220i
\(142\) −12.8908 + 3.45409i −1.08177 + 0.289861i
\(143\) 0.767551 + 0.205665i 0.0641858 + 0.0171985i
\(144\) 0.866025 + 0.500000i 0.0721688 + 0.0416667i
\(145\) −11.1103 + 0.160905i −0.922664 + 0.0133624i
\(146\) −12.9354 7.46828i −1.07055 0.618080i
\(147\) 4.24563 4.24563i 0.350174 0.350174i
\(148\) 2.03290 7.58688i 0.167103 0.623637i
\(149\) 12.7334 7.35165i 1.04316 0.602270i 0.122435 0.992476i \(-0.460930\pi\)
0.920728 + 0.390206i \(0.127596\pi\)
\(150\) −4.25591 + 2.62435i −0.347494 + 0.214277i
\(151\) 9.20528i 0.749115i −0.927204 0.374558i \(-0.877795\pi\)
0.927204 0.374558i \(-0.122205\pi\)
\(152\) −0.850297 + 3.17335i −0.0689682 + 0.257393i
\(153\) −1.33249 1.33249i −0.107725 0.107725i
\(154\) 3.90475 0.314654
\(155\) 10.1440 7.21792i 0.814789 0.579758i
\(156\) −0.733859 −0.0587557
\(157\) −14.8083 14.8083i −1.18183 1.18183i −0.979270 0.202560i \(-0.935074\pi\)
−0.202560 0.979270i \(-0.564926\pi\)
\(158\) −2.35128 + 8.77509i −0.187058 + 0.698109i
\(159\) 1.42238i 0.112802i
\(160\) −1.60387 1.55808i −0.126797 0.123177i
\(161\) 20.3902 11.7723i 1.60697 0.927787i
\(162\) −0.258819 + 0.965926i −0.0203347 + 0.0758903i
\(163\) −11.2096 + 11.2096i −0.878007 + 0.878007i −0.993328 0.115321i \(-0.963210\pi\)
0.115321 + 0.993328i \(0.463210\pi\)
\(164\) −3.11840 1.80041i −0.243506 0.140589i
\(165\) −1.68710 + 1.73668i −0.131340 + 0.135200i
\(166\) −5.37181 3.10141i −0.416933 0.240716i
\(167\) −0.601702 0.161225i −0.0465611 0.0124760i 0.235463 0.971883i \(-0.424339\pi\)
−0.282024 + 0.959407i \(0.591006\pi\)
\(168\) −3.48326 + 0.933337i −0.268739 + 0.0720085i
\(169\) −10.7919 + 6.23073i −0.830149 + 0.479287i
\(170\) 2.15947 + 3.61828i 0.165624 + 0.277510i
\(171\) −3.28530 −0.251233
\(172\) −7.28750 1.95268i −0.555667 0.148891i
\(173\) −5.26360 19.6440i −0.400184 1.49351i −0.812768 0.582588i \(-0.802040\pi\)
0.412584 0.910920i \(-0.364626\pi\)
\(174\) 4.30347 2.48461i 0.326245 0.188358i
\(175\) 4.16037 17.5441i 0.314495 1.32621i
\(176\) −0.937738 0.541403i −0.0706847 0.0408098i
\(177\) 1.71178 + 6.38845i 0.128665 + 0.480185i
\(178\) −0.570717 0.570717i −0.0427770 0.0427770i
\(179\) 4.82957 + 8.36506i 0.360979 + 0.625234i 0.988122 0.153670i \(-0.0491092\pi\)
−0.627143 + 0.778904i \(0.715776\pi\)
\(180\) 1.08987 1.95248i 0.0812345 0.145529i
\(181\) 3.35633 + 1.93778i 0.249474 + 0.144034i 0.619523 0.784978i \(-0.287326\pi\)
−0.370049 + 0.929012i \(0.620659\pi\)
\(182\) 1.87128 1.87128i 0.138709 0.138709i
\(183\) 4.99614 + 1.33871i 0.369325 + 0.0989605i
\(184\) −6.52903 −0.481327
\(185\) −17.0288 4.29956i −1.25198 0.316110i
\(186\) −2.38788 + 5.02972i −0.175088 + 0.368797i
\(187\) 1.44283 + 1.44283i 0.105510 + 0.105510i
\(188\) 1.04488 1.04488i 0.0762060 0.0762060i
\(189\) −1.80307 3.12301i −0.131154 0.227165i
\(190\) 7.12262 + 1.79837i 0.516729 + 0.130467i
\(191\) 1.39434 2.41506i 0.100891 0.174748i −0.811161 0.584823i \(-0.801164\pi\)
0.912052 + 0.410075i \(0.134497\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) −21.6043 5.78885i −1.55511 0.416690i −0.623998 0.781426i \(-0.714493\pi\)
−0.931111 + 0.364736i \(0.881159\pi\)
\(194\) 7.78908i 0.559224i
\(195\) 0.0237626 + 1.64079i 0.00170167 + 0.117499i
\(196\) 3.00212 5.19982i 0.214437 0.371415i
\(197\) 2.43296 + 9.07994i 0.173341 + 0.646919i 0.996828 + 0.0795833i \(0.0253590\pi\)
−0.823487 + 0.567335i \(0.807974\pi\)
\(198\) 0.280251 1.04591i 0.0199166 0.0743297i
\(199\) −7.24941 + 12.5563i −0.513897 + 0.890096i 0.485973 + 0.873974i \(0.338465\pi\)
−0.999870 + 0.0161221i \(0.994868\pi\)
\(200\) −3.43167 + 3.63644i −0.242655 + 0.257135i
\(201\) 1.69157i 0.119314i
\(202\) 2.02406 + 2.02406i 0.142412 + 0.142412i
\(203\) −4.63796 + 17.3091i −0.325521 + 1.21486i
\(204\) −1.63196 0.942213i −0.114260 0.0659681i
\(205\) −3.92445 + 7.03053i −0.274095 + 0.491034i
\(206\) 4.27090 7.39742i 0.297568 0.515403i
\(207\) −1.68984 6.30656i −0.117452 0.438336i
\(208\) −0.708853 + 0.189937i −0.0491501 + 0.0131697i
\(209\) 3.55734 0.246066
\(210\) 2.19958 + 7.75777i 0.151785 + 0.535337i
\(211\) 0.820503 + 1.42115i 0.0564857 + 0.0978361i 0.892886 0.450284i \(-0.148677\pi\)
−0.836400 + 0.548120i \(0.815344\pi\)
\(212\) 0.368140 + 1.37392i 0.0252839 + 0.0943609i
\(213\) −9.43675 9.43675i −0.646595 0.646595i
\(214\) 14.6119 8.43618i 0.998848 0.576685i
\(215\) −4.12990 + 16.3569i −0.281657 + 1.11553i
\(216\) 1.00000i 0.0680414i
\(217\) −6.73648 18.9143i −0.457302 1.28399i
\(218\) −7.88012 + 7.88012i −0.533709 + 0.533709i
\(219\) 14.9366i 1.00932i
\(220\) −1.18012 + 2.11416i −0.0795639 + 0.142536i
\(221\) 1.38290 0.0930241
\(222\) 7.58688 2.03290i 0.509198 0.136439i
\(223\) 4.11555 15.3595i 0.275598 1.02855i −0.679842 0.733359i \(-0.737952\pi\)
0.955440 0.295186i \(-0.0953818\pi\)
\(224\) −3.12301 + 1.80307i −0.208665 + 0.120473i
\(225\) −4.40071 2.37356i −0.293381 0.158237i
\(226\) 0.263253 0.455967i 0.0175113 0.0303305i
\(227\) 15.5412 4.16426i 1.03151 0.276392i 0.296918 0.954903i \(-0.404041\pi\)
0.734590 + 0.678511i \(0.237374\pi\)
\(228\) −3.17335 + 0.850297i −0.210160 + 0.0563123i
\(229\) 5.97098 + 10.3420i 0.394573 + 0.683421i 0.993047 0.117722i \(-0.0375591\pi\)
−0.598473 + 0.801143i \(0.704226\pi\)
\(230\) 0.211412 + 14.5978i 0.0139401 + 0.962552i
\(231\) 1.95238 + 3.38161i 0.128457 + 0.222494i
\(232\) 3.51377 3.51377i 0.230690 0.230690i
\(233\) −5.29177 + 5.29177i −0.346675 + 0.346675i −0.858870 0.512194i \(-0.828833\pi\)
0.512194 + 0.858870i \(0.328833\pi\)
\(234\) −0.366929 0.635540i −0.0239869 0.0415466i
\(235\) −2.37002 2.30235i −0.154603 0.150189i
\(236\) 3.30690 + 5.72773i 0.215261 + 0.372843i
\(237\) −8.77509 + 2.35128i −0.570003 + 0.152732i
\(238\) 6.56395 1.75880i 0.425477 0.114006i
\(239\) 11.3374 19.6370i 0.733357 1.27021i −0.222083 0.975028i \(-0.571286\pi\)
0.955440 0.295184i \(-0.0953810\pi\)
\(240\) 0.547399 2.16803i 0.0353345 0.139946i
\(241\) −3.28196 + 1.89484i −0.211410 + 0.122057i −0.601966 0.798522i \(-0.705616\pi\)
0.390557 + 0.920579i \(0.372283\pi\)
\(242\) 2.54355 9.49266i 0.163506 0.610212i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) 5.17239 0.331128
\(245\) −11.7231 6.54386i −0.748964 0.418072i
\(246\) 3.60082i 0.229580i
\(247\) 1.70479 1.70479i 0.108473 0.108473i
\(248\) −1.00473 + 5.47636i −0.0638003 + 0.347749i
\(249\) 6.20283i 0.393088i
\(250\) 8.24158 + 7.55489i 0.521244 + 0.477813i
\(251\) −9.33268 + 5.38822i −0.589073 + 0.340102i −0.764731 0.644350i \(-0.777128\pi\)
0.175658 + 0.984451i \(0.443795\pi\)
\(252\) −2.54992 2.54992i −0.160630 0.160630i
\(253\) 1.82977 + 6.82879i 0.115037 + 0.429322i
\(254\) −5.30628 9.19075i −0.332946 0.576679i
\(255\) −2.05379 + 3.67930i −0.128613 + 0.230407i
\(256\) 1.00000 0.0625000
\(257\) −6.44611 + 1.72723i −0.402097 + 0.107742i −0.454199 0.890900i \(-0.650075\pi\)
0.0521019 + 0.998642i \(0.483408\pi\)
\(258\) −1.95268 7.28750i −0.121569 0.453700i
\(259\) −14.1622 + 24.5297i −0.879998 + 1.52420i
\(260\) 0.447620 + 1.57873i 0.0277602 + 0.0979085i
\(261\) 4.30347 + 2.48461i 0.266378 + 0.153793i
\(262\) −3.68946 + 13.7692i −0.227936 + 0.850667i
\(263\) 14.4037 + 14.4037i 0.888170 + 0.888170i 0.994347 0.106177i \(-0.0338611\pi\)
−0.106177 + 0.994347i \(0.533861\pi\)
\(264\) 1.08281i 0.0666421i
\(265\) 3.05993 0.867587i 0.187970 0.0532954i
\(266\) 5.92362 10.2600i 0.363200 0.629081i
\(267\) 0.208897 0.779614i 0.0127843 0.0477116i
\(268\) 0.437811 + 1.63393i 0.0267436 + 0.0998084i
\(269\) 7.93542 13.7446i 0.483831 0.838020i −0.515996 0.856591i \(-0.672578\pi\)
0.999828 + 0.0185704i \(0.00591150\pi\)
\(270\) 2.23583 0.0323803i 0.136068 0.00197060i
\(271\) 20.3988i 1.23914i 0.784941 + 0.619570i \(0.212693\pi\)
−0.784941 + 0.619570i \(0.787307\pi\)
\(272\) −1.82022 0.487725i −0.110367 0.0295727i
\(273\) 2.55622 + 0.684938i 0.154710 + 0.0414543i
\(274\) 4.61669 7.99634i 0.278905 0.483077i
\(275\) 4.76512 + 2.57010i 0.287347 + 0.154983i
\(276\) −3.26452 5.65431i −0.196501 0.340349i
\(277\) 20.1079 20.1079i 1.20817 1.20817i 0.236547 0.971620i \(-0.423984\pi\)
0.971620 0.236547i \(-0.0760157\pi\)
\(278\) 3.73211 + 3.73211i 0.223837 + 0.223837i
\(279\) −5.54980 + 0.446894i −0.332258 + 0.0267548i
\(280\) 4.13249 + 6.92414i 0.246963 + 0.413797i
\(281\) −11.6433 −0.694580 −0.347290 0.937758i \(-0.612898\pi\)
−0.347290 + 0.937758i \(0.612898\pi\)
\(282\) 1.42734 + 0.382454i 0.0849968 + 0.0227748i
\(283\) −18.2747 + 18.2747i −1.08632 + 1.08632i −0.0904113 + 0.995905i \(0.528818\pi\)
−0.995905 + 0.0904113i \(0.971182\pi\)
\(284\) −11.5576 6.67279i −0.685818 0.395957i
\(285\) 2.00388 + 7.06755i 0.118699 + 0.418646i
\(286\) 0.397314 + 0.688167i 0.0234936 + 0.0406922i
\(287\) 9.18183 + 9.18183i 0.541986 + 0.541986i
\(288\) 0.258819 + 0.965926i 0.0152511 + 0.0569177i
\(289\) −11.6471 6.72447i −0.685125 0.395557i
\(290\) −7.96998 7.74242i −0.468013 0.454651i
\(291\) 6.74554 3.89454i 0.395431 0.228302i
\(292\) −3.86587 14.4276i −0.226233 0.844312i
\(293\) 2.37168 + 0.635490i 0.138555 + 0.0371257i 0.327430 0.944875i \(-0.393817\pi\)
−0.188875 + 0.982001i \(0.560484\pi\)
\(294\) 6.00423 0.350174
\(295\) 12.6992 7.57915i 0.739374 0.441275i
\(296\) 6.80221 3.92726i 0.395370 0.228267i
\(297\) 1.04591 0.280251i 0.0606899 0.0162618i
\(298\) 14.2023 + 3.80549i 0.822717 + 0.220446i
\(299\) 4.14946 + 2.39569i 0.239970 + 0.138547i
\(300\) −4.86508 1.15369i −0.280885 0.0666085i
\(301\) 23.5618 + 13.6034i 1.35808 + 0.784087i
\(302\) 6.50912 6.50912i 0.374558 0.374558i
\(303\) −0.740857 + 2.76492i −0.0425611 + 0.158840i
\(304\) −2.84515 + 1.64265i −0.163181 + 0.0942123i
\(305\) −0.167483 11.5646i −0.00959007 0.662187i
\(306\) 1.88443i 0.107725i
\(307\) 5.95729 22.2329i 0.340000 1.26890i −0.558345 0.829609i \(-0.688564\pi\)
0.898346 0.439290i \(-0.144770\pi\)
\(308\) 2.76108 + 2.76108i 0.157327 + 0.157327i
\(309\) 8.54181 0.485927
\(310\) 12.2768 + 2.06908i 0.697273 + 0.117516i
\(311\) 6.75999 0.383324 0.191662 0.981461i \(-0.438612\pi\)
0.191662 + 0.981461i \(0.438612\pi\)
\(312\) −0.518917 0.518917i −0.0293779 0.0293779i
\(313\) −1.78297 + 6.65414i −0.100780 + 0.376114i −0.997832 0.0658093i \(-0.979037\pi\)
0.897053 + 0.441924i \(0.145704\pi\)
\(314\) 20.9421i 1.18183i
\(315\) −5.61864 + 5.78377i −0.316574 + 0.325879i
\(316\) −7.86753 + 4.54232i −0.442583 + 0.255526i
\(317\) −6.36393 + 23.7505i −0.357434 + 1.33396i 0.519959 + 0.854191i \(0.325947\pi\)
−0.877393 + 0.479772i \(0.840720\pi\)
\(318\) −1.00578 + 1.00578i −0.0564011 + 0.0564011i
\(319\) −4.65983 2.69035i −0.260900 0.150631i
\(320\) −0.0323803 2.23583i −0.00181011 0.124987i
\(321\) 14.6119 + 8.43618i 0.815556 + 0.470861i
\(322\) 22.7423 + 6.09379i 1.26738 + 0.339594i
\(323\) 5.97995 1.60232i 0.332733 0.0891556i
\(324\) −0.866025 + 0.500000i −0.0481125 + 0.0277778i
\(325\) 3.51528 1.05192i 0.194993 0.0583502i
\(326\) −15.8528 −0.878007
\(327\) −10.7644 2.88432i −0.595275 0.159503i
\(328\) −0.931962 3.47813i −0.0514590 0.192048i
\(329\) −4.61484 + 2.66438i −0.254424 + 0.146892i
\(330\) −2.42098 + 0.0350616i −0.133270 + 0.00193008i
\(331\) −7.15518 4.13105i −0.393285 0.227063i 0.290298 0.956936i \(-0.406246\pi\)
−0.683582 + 0.729873i \(0.739579\pi\)
\(332\) −1.60541 5.99147i −0.0881083 0.328825i
\(333\) 5.55398 + 5.55398i 0.304356 + 0.304356i
\(334\) −0.311464 0.539471i −0.0170425 0.0295185i
\(335\) 3.63903 1.03178i 0.198821 0.0563722i
\(336\) −3.12301 1.80307i −0.170374 0.0983655i
\(337\) −14.8092 + 14.8092i −0.806708 + 0.806708i −0.984134 0.177427i \(-0.943223\pi\)
0.177427 + 0.984134i \(0.443223\pi\)
\(338\) −12.0368 3.22526i −0.654718 0.175431i
\(339\) 0.526506 0.0285959
\(340\) −1.03153 + 4.08549i −0.0559427 + 0.221567i
\(341\) 6.00936 0.483900i 0.325425 0.0262046i
\(342\) −2.32306 2.32306i −0.125616 0.125616i
\(343\) 2.53914 2.53914i 0.137100 0.137100i
\(344\) −3.77229 6.53380i −0.203388 0.352279i
\(345\) −12.5364 + 7.48200i −0.674936 + 0.402817i
\(346\) 10.1685 17.6123i 0.546662 0.946846i
\(347\) −23.2233 6.22265i −1.24669 0.334050i −0.425633 0.904896i \(-0.639948\pi\)
−0.821057 + 0.570846i \(0.806615\pi\)
\(348\) 4.79990 + 1.28613i 0.257301 + 0.0689437i
\(349\) 7.55294i 0.404300i 0.979355 + 0.202150i \(0.0647928\pi\)
−0.979355 + 0.202150i \(0.935207\pi\)
\(350\) 15.3474 9.46376i 0.820354 0.505859i
\(351\) 0.366929 0.635540i 0.0195852 0.0339226i
\(352\) −0.280251 1.04591i −0.0149374 0.0557472i
\(353\) −5.03312 + 18.7839i −0.267886 + 0.999765i 0.692574 + 0.721347i \(0.256477\pi\)
−0.960460 + 0.278418i \(0.910190\pi\)
\(354\) −3.30690 + 5.72773i −0.175760 + 0.304425i
\(355\) −14.5450 + 26.0570i −0.771969 + 1.38296i
\(356\) 0.807115i 0.0427770i
\(357\) 4.80514 + 4.80514i 0.254315 + 0.254315i
\(358\) −2.49997 + 9.33002i −0.132128 + 0.493107i
\(359\) −29.0183 16.7537i −1.53153 0.884228i −0.999292 0.0376313i \(-0.988019\pi\)
−0.532236 0.846596i \(-0.678648\pi\)
\(360\) 2.15127 0.609953i 0.113382 0.0321474i
\(361\) −4.10341 + 7.10732i −0.215969 + 0.374070i
\(362\) 1.00307 + 3.74350i 0.0527201 + 0.196754i
\(363\) 9.49266 2.54355i 0.498236 0.133502i
\(364\) 2.64640 0.138709
\(365\) −32.1326 + 9.11061i −1.68190 + 0.476871i
\(366\) 2.58619 + 4.47942i 0.135183 + 0.234143i
\(367\) 7.36697 + 27.4939i 0.384553 + 1.43517i 0.838871 + 0.544331i \(0.183216\pi\)
−0.454318 + 0.890840i \(0.650117\pi\)
\(368\) −4.61672 4.61672i −0.240663 0.240663i
\(369\) 3.11840 1.80041i 0.162338 0.0937257i
\(370\) −9.00095 15.0814i −0.467937 0.784047i
\(371\) 5.12931i 0.266300i
\(372\) −5.24503 + 1.86806i −0.271942 + 0.0968544i
\(373\) 11.3063 11.3063i 0.585416 0.585416i −0.350970 0.936387i \(-0.614148\pi\)
0.936387 + 0.350970i \(0.114148\pi\)
\(374\) 2.04047i 0.105510i
\(375\) −2.42193 + 10.9149i −0.125068 + 0.563641i
\(376\) 1.47769 0.0762060
\(377\) −3.52245 + 0.943837i −0.181415 + 0.0486101i
\(378\) 0.933337 3.48326i 0.0480057 0.179160i
\(379\) 29.5024 17.0332i 1.51544 0.874939i 0.515602 0.856828i \(-0.327568\pi\)
0.999836 0.0181107i \(-0.00576514\pi\)
\(380\) 3.76481 + 6.30809i 0.193131 + 0.323598i
\(381\) 5.30628 9.19075i 0.271849 0.470856i
\(382\) 2.69365 0.721761i 0.137819 0.0369285i
\(383\) −18.9269 + 5.07144i −0.967119 + 0.259139i −0.707611 0.706602i \(-0.750227\pi\)
−0.259508 + 0.965741i \(0.583560\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 6.08390 6.26271i 0.310064 0.319177i
\(386\) −11.1832 19.3699i −0.569209 0.985900i
\(387\) 5.33482 5.33482i 0.271184 0.271184i
\(388\) 5.50771 5.50771i 0.279612 0.279612i
\(389\) 18.1222 + 31.3887i 0.918834 + 1.59147i 0.801188 + 0.598412i \(0.204202\pi\)
0.117646 + 0.993056i \(0.462465\pi\)
\(390\) −1.14341 + 1.17701i −0.0578987 + 0.0596004i
\(391\) 6.15174 + 10.6551i 0.311107 + 0.538853i
\(392\) 5.79964 1.55401i 0.292926 0.0784893i
\(393\) −13.7692 + 3.68946i −0.694567 + 0.186109i
\(394\) −4.70012 + 8.14085i −0.236789 + 0.410130i
\(395\) 10.4106 + 17.4434i 0.523815 + 0.877673i
\(396\) 0.937738 0.541403i 0.0471231 0.0272065i
\(397\) −4.39783 + 16.4129i −0.220721 + 0.823742i 0.763353 + 0.645982i \(0.223552\pi\)
−0.984074 + 0.177760i \(0.943115\pi\)
\(398\) −14.0048 + 3.75257i −0.701997 + 0.188099i
\(399\) 11.8472 0.593103
\(400\) −4.99790 + 0.144794i −0.249895 + 0.00723969i
\(401\) 3.37021i 0.168300i 0.996453 + 0.0841501i \(0.0268175\pi\)
−0.996453 + 0.0841501i \(0.973182\pi\)
\(402\) −1.19612 + 1.19612i −0.0596572 + 0.0596572i
\(403\) 2.64798 3.11178i 0.131905 0.155009i
\(404\) 2.86245i 0.142412i
\(405\) 1.14596 + 1.92010i 0.0569432 + 0.0954105i
\(406\) −15.5189 + 8.95984i −0.770190 + 0.444670i
\(407\) −6.01389 6.01389i −0.298097 0.298097i
\(408\) −0.487725 1.82022i −0.0241460 0.0901141i
\(409\) −6.32831 10.9610i −0.312915 0.541984i 0.666077 0.745883i \(-0.267972\pi\)
−0.978992 + 0.203898i \(0.934639\pi\)
\(410\) −7.74634 + 2.19633i −0.382564 + 0.108469i
\(411\) 9.23338 0.455449
\(412\) 8.25075 2.21078i 0.406485 0.108917i
\(413\) −6.17291 23.0376i −0.303749 1.13361i
\(414\) 3.26452 5.65431i 0.160442 0.277894i
\(415\) −13.3439 + 3.78343i −0.655029 + 0.185722i
\(416\) −0.635540 0.366929i −0.0311599 0.0179902i
\(417\) −1.36605 + 5.09816i −0.0668957 + 0.249658i
\(418\) 2.51542 + 2.51542i 0.123033 + 0.123033i
\(419\) 22.6177i 1.10495i −0.833531 0.552473i \(-0.813684\pi\)
0.833531 0.552473i \(-0.186316\pi\)
\(420\) −3.93024 + 7.04091i −0.191776 + 0.343561i
\(421\) 8.36632 14.4909i 0.407749 0.706243i −0.586888 0.809668i \(-0.699647\pi\)
0.994637 + 0.103426i \(0.0329804\pi\)
\(422\) −0.424723 + 1.58509i −0.0206752 + 0.0771609i
\(423\) 0.382454 + 1.42734i 0.0185956 + 0.0693996i
\(424\) −0.711191 + 1.23182i −0.0345385 + 0.0598224i
\(425\) 9.16788 + 2.17405i 0.444707 + 0.105457i
\(426\) 13.3456i 0.646595i
\(427\) −18.0168 4.82758i −0.871893 0.233623i
\(428\) 16.2974 + 4.36689i 0.787767 + 0.211081i
\(429\) −0.397314 + 0.688167i −0.0191825 + 0.0332250i
\(430\) −14.4863 + 8.64578i −0.698593 + 0.416936i
\(431\) 6.50212 + 11.2620i 0.313196 + 0.542471i 0.979052 0.203609i \(-0.0652670\pi\)
−0.665856 + 0.746080i \(0.731934\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −0.147669 0.147669i −0.00709650 0.00709650i 0.703550 0.710646i \(-0.251597\pi\)
−0.710646 + 0.703550i \(0.751597\pi\)
\(434\) 8.61102 18.1378i 0.413342 0.870645i
\(435\) 2.72015 10.7734i 0.130421 0.516546i
\(436\) −11.1442 −0.533709
\(437\) 20.7189 + 5.55162i 0.991120 + 0.265570i
\(438\) 10.5617 10.5617i 0.504660 0.504660i
\(439\) −11.6906 6.74956i −0.557961 0.322139i 0.194365 0.980929i \(-0.437735\pi\)
−0.752327 + 0.658790i \(0.771069\pi\)
\(440\) −2.32941 + 0.660461i −0.111050 + 0.0314863i
\(441\) 3.00212 + 5.19982i 0.142958 + 0.247610i
\(442\) 0.977859 + 0.977859i 0.0465120 + 0.0465120i
\(443\) −3.55083 13.2519i −0.168705 0.629616i −0.997539 0.0701206i \(-0.977662\pi\)
0.828833 0.559496i \(-0.189005\pi\)
\(444\) 6.80221 + 3.92726i 0.322818 + 0.186379i
\(445\) −1.80458 + 0.0261346i −0.0855451 + 0.00123890i
\(446\) 13.7709 7.95064i 0.652072 0.376474i
\(447\) 3.80549 + 14.2023i 0.179994 + 0.671745i
\(448\) −3.48326 0.933337i −0.164569 0.0440960i
\(449\) −20.4774 −0.966386 −0.483193 0.875514i \(-0.660523\pi\)
−0.483193 + 0.875514i \(0.660523\pi\)
\(450\) −1.43341 4.79013i −0.0675717 0.225809i
\(451\) −3.37663 + 1.94950i −0.158999 + 0.0917983i
\(452\) 0.508565 0.136270i 0.0239209 0.00640959i
\(453\) 8.89162 + 2.38250i 0.417765 + 0.111940i
\(454\) 13.9339 + 8.04474i 0.653950 + 0.377558i
\(455\) −0.0856911 5.91690i −0.00401726 0.277389i
\(456\) −2.84515 1.64265i −0.133236 0.0769240i
\(457\) −11.1555 + 11.1555i −0.521833 + 0.521833i −0.918125 0.396292i \(-0.870297\pi\)
0.396292 + 0.918125i \(0.370297\pi\)
\(458\) −3.09081 + 11.5350i −0.144424 + 0.538997i
\(459\) 1.63196 0.942213i 0.0761734 0.0439787i
\(460\) −10.1727 + 10.4717i −0.474306 + 0.488246i
\(461\) 22.4461i 1.04542i −0.852510 0.522710i \(-0.824921\pi\)
0.852510 0.522710i \(-0.175079\pi\)
\(462\) −1.01062 + 3.77170i −0.0470185 + 0.175475i
\(463\) 25.0386 + 25.0386i 1.16364 + 1.16364i 0.983672 + 0.179970i \(0.0576002\pi\)
0.179970 + 0.983672i \(0.442400\pi\)
\(464\) 4.96922 0.230690
\(465\) 4.34651 + 11.6665i 0.201564 + 0.541022i
\(466\) −7.48369 −0.346675
\(467\) 15.3575 + 15.3575i 0.710659 + 0.710659i 0.966673 0.256014i \(-0.0824093\pi\)
−0.256014 + 0.966673i \(0.582409\pi\)
\(468\) 0.189937 0.708853i 0.00877982 0.0327667i
\(469\) 6.10005i 0.281674i
\(470\) −0.0478480 3.30387i −0.00220706 0.152396i
\(471\) 18.1364 10.4710i 0.835680 0.482480i
\(472\) −1.71178 + 6.38845i −0.0787910 + 0.294052i
\(473\) −5.77658 + 5.77658i −0.265608 + 0.265608i
\(474\) −7.86753 4.54232i −0.361368 0.208636i
\(475\) 13.9819 8.62176i 0.641535 0.395593i
\(476\) 5.88507 + 3.39775i 0.269742 + 0.155736i
\(477\) −1.37392 0.368140i −0.0629073 0.0168560i
\(478\) 21.9022 5.86868i 1.00178 0.268427i
\(479\) −16.0867 + 9.28763i −0.735018 + 0.424363i −0.820255 0.571998i \(-0.806169\pi\)
0.0852371 + 0.996361i \(0.472835\pi\)
\(480\) 1.92010 1.14596i 0.0876401 0.0523056i
\(481\) −5.76410 −0.262820
\(482\) −3.66055 0.980841i −0.166733 0.0446761i
\(483\) 6.09379 + 22.7423i 0.277277 + 1.03481i
\(484\) 8.51089 4.91376i 0.386859 0.223353i
\(485\) −12.4927 12.1360i −0.567263 0.551067i
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) −5.04721 18.8364i −0.228711 0.853560i −0.980884 0.194595i \(-0.937661\pi\)
0.752173 0.658966i \(-0.229006\pi\)
\(488\) 3.65743 + 3.65743i 0.165564 + 0.165564i
\(489\) −7.92642 13.7290i −0.358445 0.620845i
\(490\) −3.66230 12.9167i −0.165446 0.583518i
\(491\) 9.53654 + 5.50592i 0.430378 + 0.248479i 0.699508 0.714625i \(-0.253403\pi\)
−0.269130 + 0.963104i \(0.586736\pi\)
\(492\) 2.54617 2.54617i 0.114790 0.114790i
\(493\) −9.04505 2.42361i −0.407368 0.109154i
\(494\) 2.41094 0.108473
\(495\) −1.24085 2.07910i −0.0557722 0.0934484i
\(496\) −4.58282 + 3.16192i −0.205775 + 0.141974i
\(497\) 34.0302 + 34.0302i 1.52646 + 1.52646i
\(498\) 4.38606 4.38606i 0.196544 0.196544i
\(499\) 7.13058 + 12.3505i 0.319209 + 0.552886i 0.980323 0.197399i \(-0.0632496\pi\)
−0.661114 + 0.750285i \(0.729916\pi\)
\(500\) 0.485568 + 11.1698i 0.0217153 + 0.499528i
\(501\) 0.311464 0.539471i 0.0139152 0.0241018i
\(502\) −10.4092 2.78915i −0.464587 0.124486i
\(503\) 0.564475 + 0.151251i 0.0251687 + 0.00674393i 0.271381 0.962472i \(-0.412520\pi\)
−0.246213 + 0.969216i \(0.579186\pi\)
\(504\) 3.60614i 0.160630i
\(505\) 6.39997 0.0926870i 0.284795 0.00412452i
\(506\) −3.53484 + 6.12252i −0.157143 + 0.272179i
\(507\) −3.22526 12.0368i −0.143239 0.534575i
\(508\) 2.74673 10.2509i 0.121867 0.454812i
\(509\) −2.74514 + 4.75473i −0.121676 + 0.210750i −0.920429 0.390910i \(-0.872160\pi\)
0.798753 + 0.601660i \(0.205494\pi\)
\(510\) −4.05391 + 1.14941i −0.179510 + 0.0508968i
\(511\) 53.8633i 2.38277i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0.850297 3.17335i 0.0375415 0.140107i
\(514\) −5.77943 3.33675i −0.254920 0.147178i
\(515\) −5.21010 18.3757i −0.229585 0.809731i
\(516\) 3.77229 6.53380i 0.166066 0.287634i
\(517\) −0.414124 1.54553i −0.0182132 0.0679724i
\(518\) −27.3593 + 7.33091i −1.20210 + 0.322102i
\(519\) 20.3370 0.892695
\(520\) −0.799814 + 1.43284i −0.0350742 + 0.0628344i
\(521\) 11.7032 + 20.2706i 0.512728 + 0.888070i 0.999891 + 0.0147596i \(0.00469829\pi\)
−0.487163 + 0.873311i \(0.661968\pi\)
\(522\) 1.28613 + 4.79990i 0.0562923 + 0.210086i
\(523\) −4.83952 4.83952i −0.211617 0.211617i 0.593337 0.804954i \(-0.297810\pi\)
−0.804954 + 0.593337i \(0.797810\pi\)
\(524\) −12.3452 + 7.12749i −0.539301 + 0.311366i
\(525\) 15.8696 + 8.55937i 0.692604 + 0.373562i
\(526\) 20.3699i 0.888170i
\(527\) 9.88387 3.52022i 0.430548 0.153343i
\(528\) 0.765660 0.765660i 0.0333211 0.0333211i
\(529\) 19.6283i 0.853402i
\(530\) 2.77717 + 1.55022i 0.120633 + 0.0673372i
\(531\) −6.61381 −0.287015
\(532\) 11.4435 3.06629i 0.496141 0.132940i
\(533\) −0.683928 + 2.55246i −0.0296242 + 0.110559i
\(534\) 0.698982 0.403558i 0.0302479 0.0174636i
\(535\) 9.23592 36.5798i 0.399303 1.58148i
\(536\) −0.845786 + 1.46495i −0.0365324 + 0.0632760i
\(537\) −9.33002 + 2.49997i −0.402620 + 0.107882i
\(538\) 15.3301 4.10768i 0.660926 0.177095i
\(539\) −3.25071 5.63040i −0.140018 0.242518i
\(540\) 1.60387 + 1.55808i 0.0690195 + 0.0670489i
\(541\) −8.18815 14.1823i −0.352036 0.609745i 0.634570 0.772866i \(-0.281177\pi\)
−0.986606 + 0.163121i \(0.947844\pi\)
\(542\) −14.4241 + 14.4241i −0.619570 + 0.619570i
\(543\) −2.74043 + 2.74043i −0.117603 + 0.117603i
\(544\) −0.942213 1.63196i −0.0403970 0.0699697i
\(545\) 0.360851 + 24.9165i 0.0154572 + 1.06731i
\(546\) 1.32320 + 2.29185i 0.0566276 + 0.0980820i
\(547\) 0.898109 0.240648i 0.0384004 0.0102893i −0.239568 0.970880i \(-0.577006\pi\)
0.277968 + 0.960590i \(0.410339\pi\)
\(548\) 8.91876 2.38978i 0.380991 0.102086i
\(549\) −2.58619 + 4.47942i −0.110376 + 0.191177i
\(550\) 1.55211 + 5.18678i 0.0661821 + 0.221165i
\(551\) −14.1382 + 8.16268i −0.602306 + 0.347742i
\(552\) 1.68984 6.30656i 0.0719243 0.268425i
\(553\) 31.6442 8.47903i 1.34565 0.360565i
\(554\) 28.4369 1.20817
\(555\) 8.56043 15.3358i 0.363370 0.650967i
\(556\) 5.27800i 0.223837i
\(557\) −22.1816 + 22.1816i −0.939866 + 0.939866i −0.998292 0.0584254i \(-0.981392\pi\)
0.0584254 + 0.998292i \(0.481392\pi\)
\(558\) −4.24030 3.60830i −0.179506 0.152752i
\(559\) 5.53666i 0.234176i
\(560\) −1.97400 + 7.81822i −0.0834166 + 0.330380i
\(561\) −1.76710 + 1.02023i −0.0746069 + 0.0430743i
\(562\) −8.23304 8.23304i −0.347290 0.347290i
\(563\) −7.16118 26.7259i −0.301808 1.12636i −0.935659 0.352907i \(-0.885193\pi\)
0.633851 0.773455i \(-0.281473\pi\)
\(564\) 0.738845 + 1.27972i 0.0311110 + 0.0538858i
\(565\) −0.321144 1.13266i −0.0135106 0.0476512i
\(566\) −25.8443 −1.08632
\(567\) 3.48326 0.933337i 0.146283 0.0391965i
\(568\) −3.45409 12.8908i −0.144930 0.540887i
\(569\) −1.72914 + 2.99495i −0.0724892 + 0.125555i −0.899992 0.435907i \(-0.856428\pi\)
0.827502 + 0.561462i \(0.189761\pi\)
\(570\) −3.58056 + 6.41447i −0.149973 + 0.268673i
\(571\) −27.7131 16.0002i −1.15976 0.669586i −0.208511 0.978020i \(-0.566862\pi\)
−0.951246 + 0.308434i \(0.900195\pi\)
\(572\) −0.205665 + 0.767551i −0.00859927 + 0.0320929i
\(573\) 1.97189 + 1.97189i 0.0823768 + 0.0823768i
\(574\) 12.9851i 0.541986i
\(575\) 23.7424 + 22.4055i 0.990127 + 0.934372i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.57916 9.62555i 0.107372 0.400717i −0.891232 0.453548i \(-0.850158\pi\)
0.998603 + 0.0528315i \(0.0168246\pi\)
\(578\) −3.48084 12.9907i −0.144784 0.540341i
\(579\) 11.1832 19.3699i 0.464758 0.804984i
\(580\) −0.160905 11.1103i −0.00668120 0.461332i
\(581\) 22.3683i 0.927991i
\(582\) 7.52368 + 2.01596i 0.311866 + 0.0835644i
\(583\) 1.48769 + 0.398624i 0.0616136 + 0.0165093i
\(584\) 7.46828 12.9354i 0.309040 0.535273i
\(585\) −1.59103 0.401714i −0.0657809 0.0166088i
\(586\) 1.22767 + 2.12639i 0.0507147 + 0.0878404i
\(587\) −3.76443 + 3.76443i −0.155375 + 0.155375i −0.780514 0.625139i \(-0.785042\pi\)
0.625139 + 0.780514i \(0.285042\pi\)
\(588\) 4.24563 + 4.24563i 0.175087 + 0.175087i
\(589\) 7.84489 16.5241i 0.323243 0.680864i
\(590\) 14.3389 + 3.62039i 0.590325 + 0.149049i
\(591\) −9.40024 −0.386674
\(592\) 7.58688 + 2.03290i 0.311819 + 0.0835516i
\(593\) −27.6862 + 27.6862i −1.13694 + 1.13694i −0.147942 + 0.988996i \(0.547265\pi\)
−0.988996 + 0.147942i \(0.952735\pi\)
\(594\) 0.937738 + 0.541403i 0.0384759 + 0.0222140i
\(595\) 7.40624 13.2681i 0.303626 0.543938i
\(596\) 7.35165 + 12.7334i 0.301135 + 0.521581i
\(597\) −10.2522 10.2522i −0.419595 0.419595i
\(598\) 1.24010 + 4.62812i 0.0507116 + 0.189258i
\(599\) 13.3157 + 7.68785i 0.544066 + 0.314117i 0.746725 0.665132i \(-0.231625\pi\)
−0.202659 + 0.979249i \(0.564958\pi\)
\(600\) −2.62435 4.25591i −0.107139 0.173747i
\(601\) 27.2724 15.7457i 1.11247 0.642282i 0.172998 0.984922i \(-0.444654\pi\)
0.939467 + 0.342640i \(0.111321\pi\)
\(602\) 7.04164 + 26.2797i 0.286996 + 1.07108i
\(603\) −1.63393 0.437811i −0.0665389 0.0178291i
\(604\) 9.20528 0.374558
\(605\) −11.2619 18.8698i −0.457863 0.767167i
\(606\) −2.47896 + 1.43123i −0.100701 + 0.0581396i
\(607\) −19.6407 + 5.26271i −0.797192 + 0.213607i −0.634351 0.773045i \(-0.718733\pi\)
−0.162841 + 0.986652i \(0.552066\pi\)
\(608\) −3.17335 0.850297i −0.128696 0.0344841i
\(609\) −15.5189 8.95984i −0.628858 0.363071i
\(610\) 8.05898 8.29583i 0.326298 0.335888i
\(611\) −0.939131 0.542208i −0.0379932 0.0219354i
\(612\) 1.33249 1.33249i 0.0538627 0.0538627i
\(613\) −7.51401 + 28.0427i −0.303488 + 1.13263i 0.630751 + 0.775985i \(0.282747\pi\)
−0.934239 + 0.356647i \(0.883920\pi\)
\(614\) 19.9335 11.5086i 0.804449 0.464449i
\(615\) −5.77525 5.61036i −0.232881 0.226232i
\(616\) 3.90475i 0.157327i
\(617\) −5.30797 + 19.8096i −0.213691 + 0.797505i 0.772933 + 0.634488i \(0.218789\pi\)
−0.986623 + 0.163016i \(0.947878\pi\)
\(618\) 6.03997 + 6.03997i 0.242963 + 0.242963i
\(619\) 41.6245 1.67303 0.836514 0.547945i \(-0.184590\pi\)
0.836514 + 0.547945i \(0.184590\pi\)
\(620\) 7.21792 + 10.1440i 0.289879 + 0.407395i
\(621\) 6.52903 0.262001
\(622\) 4.78004 + 4.78004i 0.191662 + 0.191662i
\(623\) −0.753311 + 2.81139i −0.0301808 + 0.112636i
\(624\) 0.733859i 0.0293779i
\(625\) 24.9581 1.44733i 0.998323 0.0578933i
\(626\) −5.96594 + 3.44444i −0.238447 + 0.137667i
\(627\) −0.920708 + 3.43613i −0.0367695 + 0.137226i
\(628\) 14.8083 14.8083i 0.590915 0.590915i
\(629\) −12.8183 7.40062i −0.511097 0.295082i
\(630\) −8.06272 + 0.116768i −0.321227 + 0.00465214i
\(631\) −0.123258 0.0711630i −0.00490682 0.00283295i 0.497545 0.867438i \(-0.334235\pi\)
−0.502451 + 0.864605i \(0.667568\pi\)
\(632\) −8.77509 2.35128i −0.349054 0.0935288i
\(633\) −1.58509 + 0.424723i −0.0630016 + 0.0168812i
\(634\) −21.2941 + 12.2942i −0.845698 + 0.488264i
\(635\) −23.0084 5.80931i −0.913059 0.230535i
\(636\) −1.42238 −0.0564011
\(637\) −4.25612 1.14042i −0.168634 0.0451852i
\(638\) −1.39263 5.19736i −0.0551347 0.205765i
\(639\) 11.5576 6.67279i 0.457212 0.263971i
\(640\) 1.55808 1.60387i 0.0615884 0.0633985i
\(641\) 3.97989 + 2.29779i 0.157196 + 0.0907572i 0.576535 0.817073i \(-0.304405\pi\)
−0.419338 + 0.907830i \(0.637738\pi\)
\(642\) 4.36689 + 16.2974i 0.172347 + 0.643209i
\(643\) 5.92077 + 5.92077i 0.233492 + 0.233492i 0.814149 0.580656i \(-0.197204\pi\)
−0.580656 + 0.814149i \(0.697204\pi\)
\(644\) 11.7723 + 20.3902i 0.463893 + 0.803487i
\(645\) −14.7306 8.22265i −0.580018 0.323766i
\(646\) 5.36147 + 3.09545i 0.210944 + 0.121789i
\(647\) 21.9431 21.9431i 0.862673 0.862673i −0.128974 0.991648i \(-0.541169\pi\)
0.991648 + 0.128974i \(0.0411685\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) 7.16148 0.281113
\(650\) 3.22950 + 1.74186i 0.126671 + 0.0683212i
\(651\) 20.0133 1.61156i 0.784385 0.0631620i
\(652\) −11.2096 11.2096i −0.439004 0.439004i
\(653\) −35.5543 + 35.5543i −1.39135 + 1.39135i −0.569027 + 0.822319i \(0.692680\pi\)
−0.822319 + 0.569027i \(0.807320\pi\)
\(654\) −5.57209 9.65114i −0.217886 0.377389i
\(655\) 16.3356 + 27.3710i 0.638285 + 1.06947i
\(656\) 1.80041 3.11840i 0.0702943 0.121753i
\(657\) 14.4276 + 3.86587i 0.562875 + 0.150822i
\(658\) −5.14718 1.37918i −0.200658 0.0537661i
\(659\) 35.3789i 1.37817i 0.724682 + 0.689083i \(0.241987\pi\)
−0.724682 + 0.689083i \(0.758013\pi\)
\(660\) −1.73668 1.68710i −0.0676002 0.0656701i
\(661\) −15.1561 + 26.2511i −0.589503 + 1.02105i 0.404795 + 0.914408i \(0.367343\pi\)
−0.994298 + 0.106641i \(0.965990\pi\)
\(662\) −2.13839 7.98057i −0.0831108 0.310174i
\(663\) −0.357921 + 1.33578i −0.0139005 + 0.0518774i
\(664\) 3.10141 5.37181i 0.120358 0.208467i
\(665\) −7.22626 25.4866i −0.280222 0.988327i
\(666\) 7.85451i 0.304356i
\(667\) −22.9415 22.9415i −0.888299 0.888299i
\(668\) 0.161225 0.601702i 0.00623800 0.0232805i
\(669\) 13.7709 + 7.95064i 0.532414 + 0.307389i
\(670\) 3.30276 + 1.84360i 0.127597 + 0.0712246i
\(671\) 2.80035 4.85034i 0.108106 0.187245i
\(672\) −0.933337 3.48326i −0.0360043 0.134370i
\(673\) 6.24147 1.67240i 0.240591 0.0644662i −0.136509 0.990639i \(-0.543588\pi\)
0.377100 + 0.926173i \(0.376921\pi\)
\(674\) −20.9433 −0.806708
\(675\) 3.43167 3.63644i 0.132085 0.139966i
\(676\) −6.23073 10.7919i −0.239643 0.415074i
\(677\) 11.6624 + 43.5247i 0.448223 + 1.67279i 0.707284 + 0.706929i \(0.249920\pi\)
−0.259062 + 0.965861i \(0.583413\pi\)
\(678\) 0.372296 + 0.372296i 0.0142979 + 0.0142979i
\(679\) −24.3254 + 14.0443i −0.933522 + 0.538969i
\(680\) −3.61828 + 2.15947i −0.138755 + 0.0828120i
\(681\) 16.0895i 0.616550i
\(682\) 4.59143 + 3.90709i 0.175815 + 0.149610i
\(683\) 26.5615 26.5615i 1.01635 1.01635i 0.0164846 0.999864i \(-0.494753\pi\)
0.999864 0.0164846i \(-0.00524746\pi\)
\(684\) 3.28530i 0.125616i
\(685\) −5.63193 19.8635i −0.215185 0.758945i
\(686\) 3.59088 0.137100
\(687\) −11.5350 + 3.09081i −0.440089 + 0.117922i
\(688\) 1.95268 7.28750i 0.0744453 0.277833i
\(689\) 0.903981 0.521914i 0.0344389 0.0198833i
\(690\) −14.1551 3.57399i −0.538877 0.136059i
\(691\) 11.9853 20.7592i 0.455943 0.789717i −0.542799 0.839863i \(-0.682635\pi\)
0.998742 + 0.0501460i \(0.0159687\pi\)
\(692\) 19.6440 5.26360i 0.746754 0.200092i
\(693\) −3.77170 + 1.01062i −0.143275 + 0.0383904i
\(694\) −12.0212 20.8214i −0.456320 0.790370i
\(695\) 11.8007 0.170903i 0.447628 0.00648273i
\(696\) 2.48461 + 4.30347i 0.0941789 + 0.163123i
\(697\) −4.79806 + 4.79806i −0.181740 + 0.181740i
\(698\) −5.34074 + 5.34074i −0.202150 + 0.202150i
\(699\) −3.74184 6.48106i −0.141530 0.245136i
\(700\) 17.5441 + 4.16037i 0.663106 + 0.157247i
\(701\) 3.85165 + 6.67126i 0.145475 + 0.251970i 0.929550 0.368696i \(-0.120196\pi\)
−0.784075 + 0.620666i \(0.786862\pi\)
\(702\) 0.708853 0.189937i 0.0267539 0.00716870i
\(703\) −24.9251 + 6.67867i −0.940069 + 0.251891i
\(704\) 0.541403 0.937738i 0.0204049 0.0353423i
\(705\) 2.83731 1.69337i 0.106859 0.0637761i
\(706\) −16.8412 + 9.72325i −0.633826 + 0.365939i
\(707\) 2.67163 9.97067i 0.100477 0.374986i
\(708\) −6.38845 + 1.71178i −0.240093 + 0.0643326i
\(709\) 38.7764 1.45628 0.728140 0.685429i \(-0.240385\pi\)
0.728140 + 0.685429i \(0.240385\pi\)
\(710\) −28.7099 + 8.14018i −1.07746 + 0.305495i
\(711\) 9.08464i 0.340701i
\(712\) 0.570717 0.570717i 0.0213885 0.0213885i
\(713\) 35.7553 + 6.55990i 1.33905 + 0.245670i
\(714\) 6.79550i 0.254315i
\(715\) 1.72278 + 0.434978i 0.0644282 + 0.0162673i
\(716\) −8.36506 + 4.82957i −0.312617 + 0.180490i
\(717\) 16.0335 + 16.0335i 0.598784 + 0.598784i
\(718\) −8.67236 32.3657i −0.323650 1.20788i
\(719\) 12.6235 + 21.8645i 0.470777 + 0.815410i 0.999441 0.0334212i \(-0.0106403\pi\)
−0.528664 + 0.848831i \(0.677307\pi\)
\(720\) 1.95248 + 1.08987i 0.0727646 + 0.0406172i
\(721\) −30.8029 −1.14716
\(722\) −7.92719 + 2.12408i −0.295019 + 0.0790502i
\(723\) −0.980841 3.66055i −0.0364779 0.136137i
\(724\) −1.93778 + 3.35633i −0.0720169 + 0.124737i
\(725\) −24.8357 + 0.719512i −0.922374 + 0.0267220i
\(726\) 8.51089 + 4.91376i 0.315869 + 0.182367i
\(727\) 4.03984 15.0769i 0.149829 0.559171i −0.849663 0.527325i \(-0.823195\pi\)
0.999493 0.0318454i \(-0.0101384\pi\)
\(728\) 1.87128 + 1.87128i 0.0693544 + 0.0693544i
\(729\) 1.00000i 0.0370370i
\(730\) −29.1633 16.2790i −1.07938 0.602512i
\(731\) −7.10860 + 12.3125i −0.262921 + 0.455393i
\(732\) −1.33871 + 4.99614i −0.0494802 + 0.184663i
\(733\) 3.68576 + 13.7555i 0.136137 + 0.508069i 0.999991 + 0.00432676i \(0.00137726\pi\)
−0.863854 + 0.503742i \(0.831956\pi\)
\(734\) −14.2319 + 24.6504i −0.525309 + 0.909861i
\(735\) 9.35505 9.63000i 0.345066 0.355208i
\(736\) 6.52903i 0.240663i
\(737\) 1.76923 + 0.474065i 0.0651706 + 0.0174624i
\(738\) 3.47813 + 0.931962i 0.128032 + 0.0343060i
\(739\) −8.04998 + 13.9430i −0.296123 + 0.512901i −0.975246 0.221124i \(-0.929027\pi\)
0.679122 + 0.734025i \(0.262361\pi\)
\(740\) 4.29956 17.0288i 0.158055 0.625992i
\(741\) 1.20547 + 2.08794i 0.0442841 + 0.0767023i
\(742\) 3.62697 3.62697i 0.133150 0.133150i
\(743\) −30.2909 30.2909i −1.11127 1.11127i −0.992979 0.118287i \(-0.962260\pi\)
−0.118287 0.992979i \(-0.537740\pi\)
\(744\) −5.02972 2.38788i −0.184398 0.0875439i
\(745\) 28.2318 16.8494i 1.03433 0.617313i
\(746\) 15.9895 0.585416
\(747\) 5.99147 + 1.60541i 0.219216 + 0.0587389i
\(748\) −1.44283 + 1.44283i −0.0527551 + 0.0527551i
\(749\) −52.6925 30.4220i −1.92534 1.11160i
\(750\) −9.43054 + 6.00541i −0.344355 + 0.219287i
\(751\) −6.99635 12.1180i −0.255301 0.442193i 0.709677 0.704528i \(-0.248841\pi\)
−0.964977 + 0.262334i \(0.915508\pi\)
\(752\) 1.04488 + 1.04488i 0.0381030 + 0.0381030i
\(753\) −2.78915 10.4092i −0.101642 0.379334i
\(754\) −3.15814 1.82335i −0.115013 0.0664026i
\(755\) −0.298070 20.5815i −0.0108479 0.749037i
\(756\) 3.12301 1.80307i 0.113583 0.0655770i
\(757\) −12.7876 47.7239i −0.464773 1.73455i −0.657642 0.753331i \(-0.728446\pi\)
0.192869 0.981224i \(-0.438221\pi\)
\(758\) 32.9057 + 8.81705i 1.19519 + 0.320250i
\(759\) −7.06968 −0.256613
\(760\) −1.79837 + 7.12262i −0.0652337 + 0.258365i
\(761\) 28.9286 16.7019i 1.04866 0.605444i 0.126386 0.991981i \(-0.459662\pi\)
0.922274 + 0.386537i \(0.126329\pi\)
\(762\) 10.2509 2.74673i 0.371353 0.0995037i
\(763\) 38.8181 + 10.4013i 1.40531 + 0.376551i
\(764\) 2.41506 + 1.39434i 0.0873738 + 0.0504453i
\(765\) −3.02237 2.93608i −0.109274 0.106154i
\(766\) −16.9694 9.79728i −0.613129 0.353990i
\(767\) 3.43201 3.43201i 0.123923 0.123923i
\(768\) −0.258819 + 0.965926i −0.00933933 + 0.0348548i
\(769\) 37.8277 21.8398i 1.36410 0.787565i 0.373935 0.927455i \(-0.378008\pi\)
0.990167 + 0.139890i \(0.0446750\pi\)
\(770\) 8.73037 0.126437i 0.314621 0.00455647i
\(771\) 6.67351i 0.240340i
\(772\) 5.78885 21.6043i 0.208345 0.777555i
\(773\) −17.6431 17.6431i −0.634579 0.634579i 0.314634 0.949213i \(-0.398118\pi\)
−0.949213 + 0.314634i \(0.898118\pi\)
\(774\) 7.54458 0.271184
\(775\) 22.4467 16.4665i 0.806308 0.591496i
\(776\) 7.78908 0.279612
\(777\) −20.0284 20.0284i −0.718515 0.718515i
\(778\) −9.38077 + 35.0095i −0.336317 + 1.25515i
\(779\) 11.8298i 0.423846i
\(780\) −1.64079 + 0.0237626i −0.0587496 + 0.000850836i
\(781\) −12.5147 + 7.22534i −0.447810 + 0.258543i
\(782\) −3.18437 + 11.8842i −0.113873 + 0.424980i
\(783\) −3.51377 + 3.51377i −0.125572 + 0.125572i
\(784\) 5.19982 + 3.00212i 0.185708 + 0.107218i
\(785\) −33.5884 32.6294i −1.19882 1.16459i
\(786\) −12.3452 7.12749i −0.440338 0.254229i
\(787\) 27.7669 + 7.44012i 0.989784 + 0.265212i 0.717160 0.696909i \(-0.245442\pi\)
0.272624 + 0.962121i \(0.412108\pi\)
\(788\) −9.07994 + 2.43296i −0.323459 + 0.0866707i
\(789\) −17.6409 + 10.1850i −0.628031 + 0.362594i
\(790\) −4.97293 + 19.6958i −0.176929 + 0.700744i
\(791\) −1.89865 −0.0675083
\(792\) 1.04591 + 0.280251i 0.0371648 + 0.00995829i
\(793\) −0.982426 3.66646i −0.0348870 0.130200i
\(794\) −14.7154 + 8.49596i −0.522231 + 0.301510i
\(795\) 0.0460571 + 3.18021i 0.00163348 + 0.112790i
\(796\) −12.5563 7.24941i −0.445048 0.256949i
\(797\) −5.60846 20.9311i −0.198662 0.741416i −0.991288 0.131709i \(-0.957954\pi\)
0.792627 0.609707i \(-0.208713\pi\)
\(798\) 8.37726 + 8.37726i 0.296552 + 0.296552i
\(799\) −1.39230 2.41153i −0.0492560 0.0853138i
\(800\) −3.63644 3.43167i −0.128567 0.121328i
\(801\) 0.698982 + 0.403558i 0.0246973 + 0.0142590i
\(802\) −2.38310 + 2.38310i −0.0841501 + 0.0841501i
\(803\) −15.6223 4.18599i −0.551300 0.147720i
\(804\) −1.69157 −0.0596572
\(805\) 45.2079 26.9811i 1.59337 0.950960i
\(806\) 4.07277 0.327957i 0.143457 0.0115518i
\(807\) 11.2224 + 11.2224i 0.395047 + 0.395047i
\(808\) −2.02406 + 2.02406i −0.0712062 + 0.0712062i
\(809\) −21.3545 36.9870i −0.750783 1.30039i −0.947444 0.319923i \(-0.896343\pi\)
0.196660 0.980472i \(-0.436990\pi\)
\(810\) −0.547399 + 2.16803i −0.0192337 + 0.0761768i
\(811\) 13.7121 23.7500i 0.481495 0.833974i −0.518279 0.855212i \(-0.673427\pi\)
0.999774 + 0.0212371i \(0.00676048\pi\)
\(812\) −17.3091 4.63796i −0.607430 0.162760i
\(813\) −19.7038 5.27960i −0.691041 0.185164i
\(814\) 8.50492i 0.298097i
\(815\) −24.6999 + 25.4259i −0.865201 + 0.890630i
\(816\) 0.942213 1.63196i 0.0329840 0.0571300i
\(817\) 6.41513 + 23.9416i 0.224437 + 0.837611i
\(818\) 3.27577 12.2254i 0.114535 0.427450i
\(819\) −1.32320 + 2.29185i −0.0462363 + 0.0800836i
\(820\) −7.03053 3.92445i −0.245517 0.137048i
\(821\) 22.1401i 0.772695i −0.922353 0.386348i \(-0.873737\pi\)
0.922353 0.386348i \(-0.126263\pi\)
\(822\) 6.52899 + 6.52899i 0.227725 + 0.227725i
\(823\) 6.53848 24.4019i 0.227917 0.850598i −0.753298 0.657680i \(-0.771538\pi\)
0.981215 0.192919i \(-0.0617953\pi\)
\(824\) 7.39742 + 4.27090i 0.257701 + 0.148784i
\(825\) −3.71583 + 3.93756i −0.129369 + 0.137088i
\(826\) 11.9252 20.6550i 0.414929 0.718678i
\(827\) −7.76700 28.9868i −0.270085 1.00797i −0.959064 0.283189i \(-0.908607\pi\)
0.688979 0.724781i \(-0.258059\pi\)
\(828\) 6.30656 1.68984i 0.219168 0.0587259i
\(829\) 2.91941 0.101395 0.0506976 0.998714i \(-0.483856\pi\)
0.0506976 + 0.998714i \(0.483856\pi\)
\(830\) −12.1109 6.76030i −0.420375 0.234654i
\(831\) 14.2184 + 24.6271i 0.493232 + 0.854303i
\(832\) −0.189937 0.708853i −0.00658487 0.0245751i
\(833\) −8.00058 8.00058i −0.277204 0.277204i
\(834\) −4.57089 + 2.63900i −0.158277 + 0.0913812i
\(835\) −1.35053 0.340990i −0.0467369 0.0118004i
\(836\) 3.55734i 0.123033i
\(837\) 1.00473 5.47636i 0.0347285 0.189291i
\(838\) 15.9931 15.9931i 0.552473 0.552473i
\(839\) 57.3759i 1.98084i 0.138105 + 0.990418i \(0.455899\pi\)
−0.138105 + 0.990418i \(0.544101\pi\)
\(840\) −7.75777 + 2.19958i −0.267669 + 0.0758926i
\(841\) −4.30687 −0.148513
\(842\) 16.1625 4.33072i 0.556996 0.149247i
\(843\) 3.01350 11.2465i 0.103791 0.387351i
\(844\) −1.42115 + 0.820503i −0.0489181 + 0.0282429i
\(845\) −23.9272 + 14.2803i −0.823121 + 0.491258i
\(846\) −0.738845 + 1.27972i −0.0254020 + 0.0439976i
\(847\) −34.2319 + 9.17240i −1.17622 + 0.315167i
\(848\) −1.37392 + 0.368140i −0.0471805 + 0.0126420i
\(849\) −12.9221 22.3818i −0.443487 0.768141i
\(850\) 4.94539 + 8.01995i 0.169625 + 0.275082i
\(851\) −25.6412 44.4118i −0.878968 1.52242i
\(852\) 9.43675 9.43675i 0.323298 0.323298i
\(853\) 27.8840 27.8840i 0.954729 0.954729i −0.0442894 0.999019i \(-0.514102\pi\)
0.999019 + 0.0442894i \(0.0141024\pi\)
\(854\) −9.32617 16.1534i −0.319135 0.552758i
\(855\) −7.34538 + 0.106379i −0.251207 + 0.00363808i
\(856\) 8.43618 + 14.6119i 0.288343 + 0.499424i
\(857\) −13.4524 + 3.60455i −0.459524 + 0.123129i −0.481152 0.876637i \(-0.659782\pi\)
0.0216282 + 0.999766i \(0.493115\pi\)
\(858\) −0.767551 + 0.205665i −0.0262038 + 0.00702128i
\(859\) −24.4612 + 42.3681i −0.834606 + 1.44558i 0.0597439 + 0.998214i \(0.480972\pi\)
−0.894350 + 0.447367i \(0.852362\pi\)
\(860\) −16.3569 4.12990i −0.557765 0.140828i
\(861\) −11.2454 + 6.49253i −0.383242 + 0.221265i
\(862\) −3.36574 + 12.5611i −0.114638 + 0.427834i
\(863\) 50.3546 13.4925i 1.71409 0.459290i 0.737670 0.675161i \(-0.235926\pi\)
0.976422 + 0.215872i \(0.0692592\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −12.4046 43.7503i −0.421769 1.48756i
\(866\) 0.208835i 0.00709650i
\(867\) 9.50984 9.50984i 0.322971 0.322971i
\(868\) 18.9143 6.73648i 0.641993 0.228651i
\(869\) 9.83691i 0.333694i
\(870\) 9.54139 5.69452i 0.323483 0.193062i
\(871\) 1.07506 0.620688i 0.0364271 0.0210312i
\(872\) −7.88012 7.88012i −0.266855 0.266855i
\(873\) 2.01596 + 7.52368i 0.0682300 + 0.254638i
\(874\) 10.7249 + 18.5761i 0.362775 + 0.628345i
\(875\) 8.73382 39.3605i 0.295257 1.33063i
\(876\) 14.9366 0.504660
\(877\) 26.7809 7.17592i 0.904326 0.242313i 0.223453 0.974715i \(-0.428267\pi\)
0.680873 + 0.732401i \(0.261600\pi\)
\(878\) −3.49383 13.0392i −0.117911 0.440050i
\(879\) −1.22767 + 2.12639i −0.0414084 + 0.0717214i
\(880\) −2.11416 1.18012i −0.0712682 0.0397820i
\(881\) −26.9676 15.5697i −0.908560 0.524558i −0.0285927 0.999591i \(-0.509103\pi\)
−0.879968 + 0.475034i \(0.842436\pi\)
\(882\) −1.55401 + 5.79964i −0.0523262 + 0.195284i
\(883\) −35.2381 35.2381i −1.18586 1.18586i −0.978202 0.207655i \(-0.933417\pi\)
−0.207655 0.978202i \(-0.566583\pi\)
\(884\) 1.38290i 0.0465120i
\(885\) 4.03411 + 14.2281i 0.135605 + 0.478272i
\(886\) 6.85968 11.8813i 0.230456 0.399161i
\(887\) −6.00613 + 22.4152i −0.201666 + 0.752628i 0.788774 + 0.614683i \(0.210716\pi\)
−0.990440 + 0.137944i \(0.955950\pi\)
\(888\) 2.03290 + 7.58688i 0.0682196 + 0.254599i
\(889\) −19.1352 + 33.1431i −0.641773 + 1.11158i
\(890\) −1.29451 1.25755i −0.0433920 0.0421531i
\(891\) 1.08281i 0.0362754i
\(892\) 15.3595 + 4.11555i 0.514273 + 0.137799i
\(893\) −4.68923 1.25648i −0.156919 0.0420463i
\(894\) −7.35165 + 12.7334i −0.245876 + 0.425869i
\(895\) 11.0690 + 18.5465i 0.369995 + 0.619941i
\(896\) −1.80307 3.12301i −0.0602363 0.104332i
\(897\) −3.38802 + 3.38802i −0.113123 + 0.113123i
\(898\) −14.4797 14.4797i −0.483193 0.483193i
\(899\) −22.7730 + 15.7123i −0.759523 + 0.524034i
\(900\) 2.37356 4.40071i 0.0791185 0.146690i
\(901\) 2.68037 0.0892962
\(902\) −3.76614 1.00913i −0.125399 0.0336005i
\(903\) −19.2381 + 19.2381i −0.640204 + 0.640204i
\(904\) 0.455967 + 0.263253i 0.0151652 + 0.00875566i
\(905\) 7.56694 + 4.22387i 0.251534 + 0.140406i
\(906\) 4.60264 + 7.97201i 0.152913 + 0.264852i
\(907\) 38.7165 + 38.7165i 1.28556 + 1.28556i 0.937456 + 0.348102i \(0.113174\pi\)
0.348102 + 0.937456i \(0.386826\pi\)
\(908\) 4.16426 + 15.5412i 0.138196 + 0.515754i
\(909\) −2.47896 1.43123i −0.0822218 0.0474708i
\(910\) 4.12329 4.24447i 0.136686 0.140703i
\(911\) 37.0151 21.3707i 1.22636 0.708042i 0.260097 0.965582i \(-0.416245\pi\)
0.966268 + 0.257540i \(0.0829120\pi\)
\(912\) −0.850297 3.17335i −0.0281562 0.105080i
\(913\) −6.48761 1.73835i −0.214708 0.0575309i
\(914\) −15.7763 −0.521833
\(915\) 11.2139 + 2.83136i 0.370720 + 0.0936019i
\(916\) −10.3420 + 5.97098i −0.341711 + 0.197287i
\(917\) 49.6538 13.3047i 1.63971 0.439360i
\(918\) 1.82022 + 0.487725i 0.0600760 + 0.0160973i
\(919\) 13.6291 + 7.86878i 0.449584 + 0.259567i 0.707654 0.706559i \(-0.249753\pi\)
−0.258071 + 0.966126i \(0.583087\pi\)
\(920\) −14.5978 + 0.211412i −0.481276 + 0.00697004i
\(921\) 19.9335 + 11.5086i 0.656830 + 0.379221i
\(922\) 15.8718 15.8718i 0.522710 0.522710i
\(923\) −2.53481 + 9.46005i −0.0834344 + 0.311381i
\(924\) −3.38161 + 1.95238i −0.111247 + 0.0642284i
\(925\) −38.2128 9.06169i −1.25643 0.297947i
\(926\) 35.4099i 1.16364i
\(927\) −2.21078 + 8.25075i −0.0726116 + 0.270990i
\(928\) 3.51377 + 3.51377i 0.115345 + 0.115345i
\(929\) 23.9611 0.786137 0.393068 0.919509i \(-0.371414\pi\)
0.393068 + 0.919509i \(0.371414\pi\)
\(930\) −5.17604 + 11.3229i −0.169729 + 0.371293i
\(931\) −19.7257 −0.646483
\(932\) −5.29177 5.29177i −0.173338 0.173338i
\(933\) −1.74961 + 6.52965i −0.0572798 + 0.213771i
\(934\) 21.7187i 0.710659i
\(935\) 3.27264 + 3.17921i 0.107027 + 0.103971i
\(936\) 0.635540 0.366929i 0.0207733 0.0119935i
\(937\) −6.07649 + 22.6778i −0.198510 + 0.740851i 0.792820 + 0.609456i \(0.208612\pi\)
−0.991330 + 0.131395i \(0.958055\pi\)
\(938\) 4.31338 4.31338i 0.140837 0.140837i
\(939\) −5.96594 3.44444i −0.194691 0.112405i
\(940\) 2.30235 2.37002i 0.0750945 0.0773016i
\(941\) −39.3671 22.7286i −1.28333 0.740932i −0.305876 0.952071i \(-0.598949\pi\)
−0.977456 + 0.211140i \(0.932282\pi\)
\(942\) 20.2285 + 5.42021i 0.659080 + 0.176600i
\(943\) −22.7088 + 6.08481i −0.739501 + 0.198149i
\(944\) −5.72773 + 3.30690i −0.186422 + 0.107631i
\(945\) −4.13249 6.92414i −0.134430 0.225242i
\(946\) −8.16932 −0.265608
\(947\) 20.4805 + 5.48773i 0.665526 + 0.178327i 0.575739 0.817634i \(-0.304715\pi\)
0.0897873 + 0.995961i \(0.471381\pi\)
\(948\) −2.35128 8.77509i −0.0763660 0.285002i
\(949\) −9.49279 + 5.48067i −0.308149 + 0.177910i
\(950\) 15.9832 + 3.79022i 0.518564 + 0.122971i
\(951\) −21.2941 12.2942i −0.690510 0.398666i
\(952\) 1.75880 + 6.56395i 0.0570032 + 0.212739i
\(953\) 32.1879 + 32.1879i 1.04267 + 1.04267i 0.999048 + 0.0436214i \(0.0138895\pi\)
0.0436214 + 0.999048i \(0.486110\pi\)
\(954\) −0.711191 1.23182i −0.0230257 0.0398816i
\(955\) 3.03930 5.44482i 0.0983495 0.176190i
\(956\) 19.6370 + 11.3374i 0.635106 + 0.366679i
\(957\) 3.80473 3.80473i 0.122990 0.122990i
\(958\) −17.9423 4.80763i −0.579690 0.155328i
\(959\) −33.2969 −1.07521
\(960\) 2.16803 + 0.547399i 0.0699729 + 0.0176672i
\(961\) 11.0045 28.9810i 0.354984 0.934872i
\(962\) −4.07584 4.07584i −0.131410 0.131410i
\(963\) −11.9306 + 11.9306i −0.384457 + 0.384457i
\(964\) −1.89484 3.28196i −0.0610287 0.105705i
\(965\) −48.4910 12.2433i −1.56098 0.394127i
\(966\) −11.7723 + 20.3902i −0.378767 + 0.656044i
\(967\) −9.96935 2.67128i −0.320593 0.0859025i 0.0949340 0.995484i \(-0.469736\pi\)
−0.415527 + 0.909581i \(0.636403\pi\)
\(968\) 9.49266 + 2.54355i 0.305106 + 0.0817529i
\(969\) 6.19090i 0.198880i
\(970\) −0.252213 17.4151i −0.00809806 0.559165i
\(971\) 9.88883 17.1280i 0.317348 0.549662i −0.662586 0.748986i \(-0.730541\pi\)
0.979934 + 0.199323i \(0.0638744\pi\)
\(972\) −0.258819 0.965926i −0.00830162 0.0309821i
\(973\) 4.92616 18.3847i 0.157925 0.589385i
\(974\) 9.75046 16.8883i 0.312425 0.541136i
\(975\) 0.106258 + 3.66776i 0.00340299 + 0.117462i
\(976\) 5.17239i 0.165564i
\(977\) 2.02295 + 2.02295i 0.0647198 + 0.0647198i 0.738726 0.674006i \(-0.235428\pi\)
−0.674006 + 0.738726i \(0.735428\pi\)
\(978\) 4.10302 15.3127i 0.131200 0.489645i
\(979\) −0.756863 0.436975i −0.0241894 0.0139658i
\(980\) 6.54386 11.7231i 0.209036 0.374482i
\(981\) 5.57209 9.65114i 0.177903 0.308137i
\(982\) 2.85007 + 10.6366i 0.0909495 + 0.339428i
\(983\) −9.55770 + 2.56098i −0.304843 + 0.0816825i −0.407998 0.912983i \(-0.633773\pi\)
0.103155 + 0.994665i \(0.467106\pi\)
\(984\) 3.60082 0.114790
\(985\) 5.73371 + 20.2224i 0.182691 + 0.644341i
\(986\) −4.68206 8.10957i −0.149107 0.258261i
\(987\) −1.37918 5.14718i −0.0438999 0.163837i
\(988\) 1.70479 + 1.70479i 0.0542367 + 0.0542367i
\(989\) −42.6594 + 24.6294i −1.35649 + 0.783169i
\(990\) 0.592728 2.34756i 0.0188381 0.0746103i
\(991\) 2.45475i 0.0779777i 0.999240 + 0.0389888i \(0.0124137\pi\)
−0.999240 + 0.0389888i \(0.987586\pi\)
\(992\) −5.47636 1.00473i −0.173875 0.0319001i
\(993\) 5.84218 5.84218i 0.185396 0.185396i
\(994\) 48.1260i 1.52646i
\(995\) −15.8019 + 28.3086i −0.500954 + 0.897444i
\(996\) 6.20283 0.196544
\(997\) 18.6855 5.00675i 0.591774 0.158565i 0.0495102 0.998774i \(-0.484234\pi\)
0.542264 + 0.840208i \(0.317567\pi\)
\(998\) −3.69106 + 13.7752i −0.116839 + 0.436047i
\(999\) −6.80221 + 3.92726i −0.215212 + 0.124253i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.be.b.37.15 yes 64
5.3 odd 4 930.2.be.a.223.12 64
31.26 odd 6 930.2.be.a.367.12 yes 64
155.88 even 12 inner 930.2.be.b.553.15 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.be.a.223.12 64 5.3 odd 4
930.2.be.a.367.12 yes 64 31.26 odd 6
930.2.be.b.37.15 yes 64 1.1 even 1 trivial
930.2.be.b.553.15 yes 64 155.88 even 12 inner